Agent-Based Models for Two Stocks with Superhedging

We propose an agent-based, non-probabilistic framework for modeling the joint evolution of two discounted asset prices expressed in units of a third asset acting as numeraire. The framework is based on a trajectorial superhedging theory, in which pricing, arbitrage, and null events are defined purely in financial terms, without reference to probability measures or martingale assumptions. A central necessary theoretical requirement is that the global property (L)-a.e. holds, ensuring consistency of the model construction. Admissible price evolutions are described by multidimensional trajectory sets generated from observable price movements and operational rebalancing rules representing a prescribed class of agents. Within a fixed trajectory set, relative price bounds between the two assets are obtained via superhedging and subhedging by means of self-financing portfolios that trade one asset against the other.